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A093140
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Expansion of (1-6*x)/((1-x)*(1-10*x)).
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2
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1, 5, 45, 445, 4445, 44445, 444445, 4444445, 44444445, 444444445, 4444444445, 44444444445, 444444444445, 4444444444445, 44444444444445, 444444444444445, 4444444444444445, 44444444444444445, 444444444444444445
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OFFSET
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0,2
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COMMENTS
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Second binomial transform of 4*A001045(3n)/3+(-1)^n. Partial sums of A093141. A convex combination of 10^n and 1. In general the second binomial transform of k*Jacobsthal(3n)/3+(-1)^n is 1, 1+k, 1+11k, 1+111k, ... This is the case for k=4.
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LINKS
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FORMULA
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G.f.: (1-6*x)/((1-x)*(1-10*x)).
a(n) = 4*10^n/9 + 5/9.
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MATHEMATICA
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CoefficientList[Series[(1-6x)/((1-x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{11, -10}, {1, 5}, 30] (* or *) Join[{1}, Table[FromDigits[PadLeft[{5}, n, 4]], {n, 30}]] (* Harvey P. Dale, Dec 17 2022 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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